A cylindrical rod of length l, thermal conductivity K and area of cross section A has one end in the furnace at temperature T1 and the other end in surrounding at temperature T2. Surface of the rod exposed to the surrounding has emissivity e. Also T2=Ts+Δ T and Ts gg Δ T. If T1-Ts propto Δ T, then the proportionality constant is

Question

A cylindrical rod of length l, thermal conductivity K and area of cross section A has one end in the furnace at temperature T1 and the other end in surrounding at temperature T2. Surface of the rod exposed to the surrounding has emissivity e. Also T2=Ts+Δ T and Ts gg Δ T. If T1-Ts propto Δ T, then the proportionality constant is (A) ((1+2 e σ ℓ Ts3/k)) (B) (1+(4 e σ ℓ Ts2/k)) (C) (1+(4 e σ ℓ Ts3/k)) (D) k(1+4 e σ 1 Ts)

Tardigrade Admin · Accepted Answer

Correct answer is (c) (1+(4 e σ ℓ Ts3/k))

$(\frac{1 + 2 e σ ℓ T _{s}^{3}}{k})$

$(1 + \frac{4 e σ ℓ T _{s}^{2}}{k})$

$(1 + \frac{4 e σ ℓ T _{s}^{3}}{k})$

$k (1 + 4 e σ 1 T_{s})$

Correct answer is (c) $(1 + \frac{4 e σ ℓ T _{s}^{3}}{k})$

(k1+2eσℓTs3​​)

(1+k4eσℓTs2​​)

(1+k4eσℓTs3​​)

k(1+4eσ1Ts​)

Correct answer is (c) (1+k4eσℓTs3​​)

$(\frac{1 + 2 e σ ℓ T _{s}^{3}}{k})$

$(1 + \frac{4 e σ ℓ T _{s}^{2}}{k})$

$(1 + \frac{4 e σ ℓ T _{s}^{3}}{k})$

$k (1 + 4 e σ 1 T_{s})$

Correct answer is (c) $(1 + \frac{4 e σ ℓ T _{s}^{3}}{k})$